Some properties of solutions to multiterm fractional boundary value problems with \(p\)-Laplacian operator. (English) Zbl 1471.34019
This article deals with a class of multi-point boundary value problems for non-linear multi-term fractional differential equations with \(p\)-Laplacian operator, and is aimed at studying some properties of positive solutions to \(m\)-point boundary value problems in Riemann-Liouville fractional-order sense including the existence, uniqueness, and the continuous dependency on boundary conditions with the help of the well-known contraction mapping principle.
This study is organized as follows. Section 2 is devoted to some necessary definitions and preliminary results from fractional calculus and fractional differential equations which will be used to prove the main results. In Section 3, the main results i.e., existence and uniqueness of positive solutions to \(p\)-Laplacian fractional boundary value problem and continuous dependence of them on the perturbations with respect to the coefficients in \(m\)-point boundary conditions are established. Finally, in Section 4, two illustrative examples are provided to demonstrate the efficiency of the established results.
This study is organized as follows. Section 2 is devoted to some necessary definitions and preliminary results from fractional calculus and fractional differential equations which will be used to prove the main results. In Section 3, the main results i.e., existence and uniqueness of positive solutions to \(p\)-Laplacian fractional boundary value problem and continuous dependence of them on the perturbations with respect to the coefficients in \(m\)-point boundary conditions are established. Finally, in Section 4, two illustrative examples are provided to demonstrate the efficiency of the established results.
Reviewer: Ismail Huseynov (Mersin)
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
multi-term fractional differential equations; \(p\)-Laplacian; Banach’s fixed-point theorem; \(m\)-point boundary value problem; Riemann-Liouville fractional derivativeReferences:
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